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A 10 GHz signal propagates in a waveguide with a phase velocity of 4 x 108 m/s. If the signal produces standing wave in the guide, then the distance between successive minimal will be
- a)10 mm
- b)20 mm
- c)30 mm
- d)40 mm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A 10 GHz signal propagates in a waveguide with a phase velocity of 4 x...
f = 10 GHz, v = 4 x 108 m/sec,
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A 10 GHz signal propagates in a waveguide with a phase velocity of 4 x...
Given information:
- Frequency of the signal: 10 GHz (10 x 10^9 Hz)
- Phase velocity of the waveguide: 4 x 10^8 m/s
Concept:
- In a waveguide, the standing wave pattern is formed when the incident wave reflects back and interferes with itself.
- Standing waves are formed by the superposition of two waves traveling in opposite directions.
- The distance between successive nodes (or minima) of a standing wave is given by λ/2, where λ is the wavelength of the wave.
Solution:
- The phase velocity of the waveguide is given by the equation:
Phase velocity (v) = Frequency (f) x Wavelength (λ)
- Rearranging the equation, we get:
Wavelength (λ) = v / f
- Substituting the given values, we have:
Wavelength (λ) = (4 x 10^8 m/s) / (10 x 10^9 Hz)
= 0.04 m = 40 mm
Conclusion:
- The distance between successive minima (nodes) in the waveguide is equal to half the wavelength of the signal.
- Therefore, the distance between successive minima is 40 mm, which corresponds to option 'B'.
- Frequency of the signal: 10 GHz (10 x 10^9 Hz)
- Phase velocity of the waveguide: 4 x 10^8 m/s
Concept:
- In a waveguide, the standing wave pattern is formed when the incident wave reflects back and interferes with itself.
- Standing waves are formed by the superposition of two waves traveling in opposite directions.
- The distance between successive nodes (or minima) of a standing wave is given by λ/2, where λ is the wavelength of the wave.
Solution:
- The phase velocity of the waveguide is given by the equation:
Phase velocity (v) = Frequency (f) x Wavelength (λ)
- Rearranging the equation, we get:
Wavelength (λ) = v / f
- Substituting the given values, we have:
Wavelength (λ) = (4 x 10^8 m/s) / (10 x 10^9 Hz)
= 0.04 m = 40 mm
Conclusion:
- The distance between successive minima (nodes) in the waveguide is equal to half the wavelength of the signal.
- Therefore, the distance between successive minima is 40 mm, which corresponds to option 'B'.
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